Sensitivity study on three different S_N order schemes of the discrete ordinates method for two-compartment enclosure fire

摘要

This paper presents a numerical study on the applicability of discrete ordinates method (DOM) for accounting the global radiative heat transfer of an enclosure fire in a two-compartment structure. The DOM employs Gaussian quadrature technique to approximate the radiative transfer equation (RTE). It is anticipated that by increasing the division of the solid angle and thereafter having more discrete radiation intensities, more accurate predictions could be attained. However, employing the higher approximation order (i.e. S_8 scheme) requires 3.33 times the computational storage compared with the S_4 approximation. Owing to the possible constraints of the computational storage capacity in personal computers, the approximation order should be chosen carefully a priori. The optimum choice of approximation order is investigated through sensitivity numerical studies of the S_4, S_6 and S_8 approximations, which approximations correspond to 24, 48 and 80 fluxes, respectively. The predicted temperatures of the three approximations are compared alongside with experimental data reported by Nielsen and Fleischmann (Fire Engineering Research Report, 2000). Contribution of soot particles to the radiation has also been considered by incorporating the model of Moss et al. (Combust Flame 1995; 101:491-500) and that of Syed et al. model (Proceedings of the Combustion Institute, vol. 23, 1990). The study revealed that S_4 approximation yields lower temperature values compared with S_6 and S_8, especially at the near field of the flame. Nevertheless, no appreciable difference could be found for the predicted temperatures between S_6 and S_8 approximations. For the current study of a weakly sooting flame, such as LPG fuel, S_6 approximation has demonstrated to be an optimum choice for accounting the global radiative heat transfer in an enclosure fire.